Astrophysical Limits on the Evolution of Dimensionless Physical Constants over Cosmological Time

We report new upper limits on any possible long-term time variation of the ratio of the electron to proton masses, $(m_e\mathrm{/}{m}_p)$, the fine-structure constant, ($\alpha$), and the quantity ${\alpha }^2{g}_p(m_e\mathrm{/}{m}_p)$, where $g_p$ is the proton gyromagnetic ratio. These limits are based on extremely high precision observations of H${}_2$, Si${}^{3+}$, C${}^0$ and H${}^0$ in high-redshift quasar absorption lines. They amount to 95% confidence ranges of $(-7.6\to 9.7) \times 10^{-14}$yr$^{-1}$for($m_e/m_p$),$(-4.6\to 4.2)\times 10^{-14}$yr$^{-1}$for$\alpha$and$(-2.2\to 4.2) \times 10^{-15}$yr$^{-1}$for$\alpha^2 g_p(m_e/m_p)$, where the elapsed time has been computed for a cosmology with \hnought = 75 km s${}^{-1}$ Mpc${}^{-1}$ and \qnought = 0.5.